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On partitions of discrete boxes
2002
Discrete Mathematics
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We prove that any partition of an n-dimensional discrete box into nontrivial sub-boxes must consist of at least 2 n sub-boxes, and consider some extensions of this theorem. ...
We are also grateful to Jeff Kahn for suggesting the point of view taken in subsection 2.4. ...
Theorem 1 Let A be an n-dimensional discrete box, and let {B 1 , B 2 , . . . , B m } be a partition of A into nontrivial sub-boxes. Then m ≥ 2 n . Proof. ...
doi:10.1016/s0012-365x(02)00428-4
fatcat:gsi3xpnyhnfthcf5lqhqcn5spq
On Partitions of Two-Dimensional Discrete Boxes
[article]
2018
arXiv
pre-print
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Let A and B be finite sets and consider a partition of the discrete box A × B into sub-boxes of the form A' × B' where A' ⊂ A and B' ⊂ B. ...
We show that a partition of A × B that has the (k, ℓ)-piercing property must consist of at least (k-1)+(ℓ-1)+ 2√((k-1)(ℓ-1)) sub-boxes. ...
Acknowledgments We thank Ron Holzman for pointing out a mistake in an earlier version of this paper. ...
arXiv:1812.08396v1
fatcat:eblbosvmcvdz3j765y5g6kmgym
On the number of minimal partitions of a box into boxes
2006
Discrete Mathematics
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The number of minimal partitions of a box into proper boxes is examined. ...
At the present stage of investigations this problem seems to be out of reach, as we know little on the structure of the minimal partitions. ...
to F satisfies one of the following two relations:
Lemma 6. ...
doi:10.1016/j.disc.2005.10.027
fatcat:7bseg7ttpzccvjbjr6paxqmjcy
Performing large full-wave simulations by means of a parallel MLFMA implementation
2013
2013 IEEE Antennas and Propagation Society International Symposium (APSURSI)
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The data structures of the MLFMAtree are partitioned according to the so-called hierarchical partitioning scheme, while the radiation patterns are partitioned in a blockwise way. ...
To test the implementation of the algorithm, a full-wave simulation of a canonical example with more than 50 millions of unknowns has been performed. ...
This method discretizes the scattering problem into a set of N linear equations, with N the number of unknowns on the discretized surface(s) of the scatterer(s). ...
doi:10.1109/aps.2013.6711598
fatcat:uhznxf3oznflvm6kitx2ec7eie
Hierarchical parallelization of the multilevel fast multipole algorithm (MLFMA)
2013
Proceedings of the IEEE
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This paper presents the hierarchical partitioning strategy, which provides a very efficient parallelization of MLFMA on distributed-memory architectures. ...
We discuss the advantages of the hierarchical strategy over previous approaches and demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. ...
One of the major advances in the parallelization of MLFMA is the development of the hierarchical strategy, which is based on the simultaneous partitioning of boxes and field samples among processors at ...
doi:10.1109/jproc.2012.2222331
fatcat:wvgih5zlmbdlhenmccrvu4mywa
Range-Box Plotting Relating to Discrete Distribution
2018
MATEMATIKA
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The new modication of box plot is not based on the asymmetrical shape of distribution but more on the spread of the data and partitioning data into range measure. ...
The existing box plot is constructed using ve values of statistics calculated from either the discrete or continous data. ...
Table 3 shows that the standard classical box plot will not look at the partitional of data, but really on the existance of outliers. ...
doi:10.11113/matematika.v34.n2.935
fatcat:wdmyh6jjtbdajlpim2rgzswmu4
Simulating Microbial Community Patterning Using Biocellion
[chapter]
2014
Msphere
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Biocellion further accelerates large scale, high resolution simulations using cluster computers by partitioning the work to run on multiple compute nodes. ...
Biocellion is a highperformance software framework for accelerating discrete agent-based simulation of biological systems with millions to trillions of cells. ...
The original yeast patterning model [5] partitions the simulation domain on top of the agarose cylinder into a set of fixed size cubic boxes (a box width is 5 μm), and a cell takes a single box. ...
doi:10.1007/978-1-4939-0554-6_16
pmid:24838890
fatcat:kmmuib5y6van5d4cgrgckh3efq
The maximum discrete surface-to-volume ratio of space-filling curve partitions
[article]
2021
arXiv
pre-print
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This framework thus has the potential to guide the design of better load balancing algorithms on the long term. ...
We investigate the surface-to-volume ratio of space-filling curve partitions for adaptive grids and derive the maximum surface-to-volume ratio as a function of the number of cells in the partition. ...
A fundamental goal in this project is the effective parallelisation of a dynamically adaptive mesh refinement solver for wave questions which uses the Peano space-filling curve. ...
arXiv:2106.12856v1
fatcat:vef5pujombhebbmjbmt4fid46i
Biocellion: accelerating computer simulation of multicellular biological system models
2014
Bioinformatics
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Availability and implementation: Biocellion runs on x86 compatible systems with the 64 bit Linux operating system and is freely available for academic use. ...
Discrete agentbased modeling (in combination with high-resolution grids to model the extracellular environment) is a popular approach for building biological system models. ...
The extracellular space is partitioned into a set of cubical grid boxes. ...
doi:10.1093/bioinformatics/btu498
pmid:25064572
pmcid:PMC4609016
fatcat:j4zdhyz7vfcqzn6az6h3zayfse
Enabling Space Filling Curves Parallel Mesh Partitioning In Alya
2017
Zenodo
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In this paper we focus on the mesh partitioning, presenting the work carried out in the context of a PRACE Preparatory Access Project to enable a Space Filling Curve (SFC) based partitioner in the computational ...
In particular, we have run our tests on the MareNostrum III supercomputer of the Barcelona Supercomputing Center. ...
The sequential and parallel executions of the algorithm produce an almost identical partition if the grid used to discretize the bounding box is the same. ...
doi:10.5281/zenodo.826103
fatcat:zsub22ti7jgffg2gztcziaguwu
Optimistic planning for continuous-action deterministic systems
2013
2013 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)
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Experiments on three problems show SOOP reliably ranks among the best algorithms, fully dominating competing methods when the problem requires both long horizons and fine discretization. ...
SOOP can be used parameter-free at the cost of more model calls, but we also propose a more practical variant tuned by a parameter α, which balances finer discretization with longer planning horizons. ...
The hierarchical partition splits at each depth d the considered box along dimension k = d, into M subboxes: one for each discrete action. So, for OPD the depth in the tree is equal to the time step. ...
doi:10.1109/adprl.2013.6614991
dblp:conf/adprl/BusoniuDMB13
fatcat:em4v6xs5zjcwtbs7oc6hub4wsq
FAUST $^{\mathsf 2}$ : Formal Abstractions of Uncountable-STate STochastic Processes
[chapter]
2015
Lecture Notes in Computer Science
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FAUST 2 allows refining the outcomes of the verification procedures over the concrete dtMP in view of the quantified and tunable error, which depends on the dtMP dynamics and on the given formula. ...
FAUST 2 is a software tool that generates formal abstractions of (possibly non-deterministic) discrete-time Markov processes (dtMP) defined over uncountable (continuous) state spaces. ...
Left: obtained uniform partition of the safe set, along with optimal safety probability for each partition set (color bar on the right). ...
doi:10.1007/978-3-662-46681-0_23
fatcat:qqltkzrnkvhdvkq6m7ld7ur6dq
Sylvester's bijection between strict and odd partitions
2004
Discrete Mathematics
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We show that Sylvester's bijection between strict partitions and odd ones can be obtained by an appropriate coding of partitions. ...
The contents of the boxes may be considered as materializing a ribbon made of two parts, the top one being described by its vertical steps, the bottom one, by its horizontal steps, each number being the ...
As a by-product, one obtains a statistics on odd partitions which generalizes the restriction of an identity of Bousquet-Melou and Eriksson to strict partitions (cf. [3] ). ...
doi:10.1016/j.disc.2002.02.001
fatcat:gkjbf2gs7rhedlvfbcgdnzj3ry
Fast and accurate solutions of extremely large scattering problems involving three-dimensional canonical and complicated objects
2009
2009 Computational Electromagnetics International Workshop
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We present fast and accurate solutions of extremely large scattering problems involving three-dimensional metallic objects discretized with hundreds of millions of unknowns. ...
Various examples involving canonical and complicated objects are presented in order to demonstrate the feasibility of accurately solving large-scale problems on relatively inexpensive computing platforms ...
At this frequency, the size of the box corresponds to 875λ, and its discretization with the RWG functions on λ/10 triangles leads to matrix equations involving 174,489,600 unknowns. ...
doi:10.1109/cem.2009.5228112
fatcat:4iiqsuesvrgofkdbpn74g4vodu
How many is different? Answer from ideal Bose gas
2014
Journal of Physics, Conference Series
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2013 pre-print arXiv:1310.5580v1 fatcat:d443dgdu25fzlaraiyaogd5gem
We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a 'boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular ...
We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. ...
This work was supported by the Sogang University Research Grant of 201310030.01. ...
doi:10.1088/1742-6596/490/1/012018
fatcat:jqxnno5kz5dztjvwjnq4t7amvm
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